Análisis predictivo del rendimiento en Cálculo Diferencial a partir de evaluaciones diagnósticas y propedéuticas en estudiantes de Ingeniería
Predictive Analysis of Performance in Differential Calculus Based on Diagnostic and Preparatory Assessments in Engineering Students
DOI:
https://doi.org/10.5281/zenodo.17526217Keywords:
Diagnostic Assessment, Longitudinal Analysi, Multiple Regression, Mathematics in Engineering, Statistical AnalysisAbstract
The learning of mathematics in engineering constitutes the foundation for developing competencies in logical reasoning, modeling, and problem-solving. Considering its importance, the present study aims to analyze the impact of diagnostic and introductory assessments as predictors of performance in Differential Calculus among first-year engineering students at the Tecnológico de Estudios Superiores de Ecatepec (TESE). Three evaluation stages were applied: initial exam (EI), assessment at the end of the preparatory course (EC), and final evaluation of the Differential Calculus course (ED). The results showed a significant positive correlation among the phases, with a progressive increase in grades and large effect sizes according to the t-test and Cohen’s d index. The multiple linear regression model explained 61.6% of the variability in final performance, confirming the relevance of EI and EC as reliable predictors. These findings validate the usefulness of implementing early diagnostics and preparatory courses as tools to identify at-risk students and strengthen teaching strategies.
References
Akinwande, M., Dikko, H. & Samson, A. (2015). Variance Inflation Factor: As a condition for the inclusion of suppressor variable(s) in regression analysis. Open Journal of Statistics, 5(7), 754–767. https://doi.org/10.4236/ojs.2015.57075
De Winter, J. & Dodou, D. (2011). Predicting academic performance in engineering using high school exam scores. International Journal of Engineering Education, 27(6), 1343–1351. https://www.ijee.ie/articles/Vol27-6/19_ijee2519ns.pdf
Escalante C. (2010). Prueba de hipótesis frente a intervalos de confianza. Ciencia y Tecnología para la salud Visual y Ocular, 8(2), 145-149.
Eisinga, R., Heskes, T., Pelzer, B., & Te Grotenhuis, M. (2017). Exact p-values for pairwise comparison of Friedman rank sums, with application to comparing classifiers. BMC Bioinformatics, 18(1), 68.
García, M. (2025). Classification of common mathematical errors using the AHP process for formative assessment in engineering students. Education Sciences, 15(7), 827. https://doi.org/10.3390/educsci15070827
González A. & Pazmiño M. (2015). Cálculo e interpretación del Alfa de Cronbach para el caso de validación de la consistencia interna de un cuestionario, con dos posibles escalas tipo Likert. SSOAR Open Access Repository. 2(1), 62-67.
Hair, J., Black, W., Babin, B., & Anderson, R. (2019). Multivariate data analysis (8th ed.). Cengage Learning.
Hieb, J., Lyle, K., Ralston, P. & Chariker, L. (2015). Predicting performance in a first engineering calculus course. International Journal of Mathematical Education in Science and Technology, 46(1), 40–55. https://doi.org/10.1080/0020739X.2014.936976
Inzunsa S. & Jiménez J. (2013). Caracterización del razonamiento estadístico de estudiantes universitarios acerca de las pruebas de hipótesis. Revista latinoamericana de investigación matemática educativa, 6(2), 179-211. https://doi.org/10.12802/relime.13.1622
Kim, T. (2015). T test as a parametric statistic. Korean Journal of Anesthesiology, 68(6), 540–546. https://doi.org/10.4097/kjae.2015.68.6.540
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863
Ledesma, R., Molina G. & Valero P. (2002). Análisis de consistencia interna mediante Alfa de Cronbach: un programa basado en gráficos dinámicos. Psico-USF, 7(2), 143-152.
Lee, S. Harrison, M., Pell, G. & Robinson, C. (2008). Predicting performance of first year engineering students and the importance of assessment tools therein. Journal of the Higher Education Academy, 3(1), 44–51. https://doi.org/10.11120/ened.2008.03010044
Legendre, P. (2005). Species associations: The Kendall coefficient of concordance revisited. Journal of Agricultural, Biological, and Environmental Statistics, 10(2), 226–245. https://doi.org/10.1198/108571105X46642
Mahata, A., Mohd, Z., Mistima, S. & Razali, N. (2025). An Early Detection of Students Mathematical Competency in Engineering. Jurnal Kejuruteraan, 37(4), 107–118. https://www.ukm.my/jkukm/wp-content/uploads/2025/3704/07.pdf
Oviedo, H. & Campo, A. (2005). Aproximación del coeficiente alfa de Cronbach. Revista colombiana de Psiquiatría, XXXIV (4), 572-580.
Ozili, P. (2023). The acceptable R-squared in empirical social science research. Munich Personal RePEc Archive (MPRA) Paper No. 115769. https://mpra.ub.uni-muenchen.de/115769
Quevedo, F. (2011). Medidas de tendencia central y dispersión. Medware, 9(3), 1-6.
Razali, N. & Wah, Y. (2011). Power comparisons of Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors and Anderson–Darling tests. Journal of Statistical Modeling and Analytics, 2(1), 21–33.
Ryan, O., Sajadi, S., Barrera, S. & Tavakoli, R. (2025). Understanding the Effects of a Math Placement Exam on Calculus 1 Enrollment and Engineering Persistence. Education Sciences, 15(2), 154. https://doi.org/10.3390/educsci15020154
Sullivan, G. & Feinn, R. (2012). Using effect size-or why the p value is not enough. Journal of Graduate Medical Education, 4(3), 279–282. https://doi.org/10.4300/JGME-D-12-00156.1
Tomczak, M., & Tomczak, E. (2014). The need to report effect size estimates revisited: An overview of some recommended measures of effect size. Trends in Sport Sciences, 1(21), 19–25.
Tuapanta, D., Duque, V. & Mena, R. (2017). Alfa de Cronbach para validar un cuestionario de uso de TIC en docentes universitarios. Descubre, 37–48. Recuperado de https://dspace.espoch.edu.ec/handle/123456789/9807
Downloads
Published
How to Cite
Conference Proceedings Volume
Section
License
Copyright (c) 2025 María de la Luz Delgadillo Torres, Mariana Bárcenas Castañeda , María de los Ángeles Vargas Hernández, Arturo Aguilar Pérez
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
